Abstract
The aim of this study was to formulate and analyse a model of ontogenetic growth cessation in pigs. The cessation of growth when an animal reaches its species-specific size in ontogeny is still a problem. Systemic factors that contribute to this process are unknown. The focus of the research is an analysis of the growth dynamic that explains some aspects of the problem.
 
 The method applied to meet the purpose of the study was mathematical modelling. To enhance the understanding of the growth trajectories in ontogeny an analytical model of growth in pigs was built. The model was formulated as a hybrid dynamic system with discrete-time and continuum equations. The novelty of the study is a concept of ontogenetic growth in the pig. Both a new modelling technique, and new variables are introduced. A central theme of the study is an analysis of the growth trajectory bifurcation, and a description of the two emerged growth trajectories. A reading of a normal form of bifurcation applied to the growth trajectory bifurcation has been offered.
 
 The results suggest that ontogenetic growth in pigs is not continuous. The growth trajectory has bifurcation at the point the animals attain their individual maximum weight. At this point, two new growth trajectories emerge. On one trajectory, animals continue to grow till a species maximum weight is reached. On other trajectory, animals continue to live till obtainable life span is attained. The emerged trajectories are genetic channels that open the way to grow for the certain phenotypes. Ontogenetic growth stops when the feed conversion coefficient grows into infinity.
Highlights
The aim of this study is to investigate some aspects of ontogenetic growth in pigs by analysing dynamic of growth from 30 kg live weight up to the maximum weight
Our findings support the opinion that animals have systemic size regulating mechanisms, which impose a certain limit on growth, that results in a species-specific size. The opinion that these mechanisms are independent of growth rate and development time (Nijhout, 2015) the model does not support
Both growth rate and development time in growth regulation are involved. This subtle, implicit involvement of the traits is due to dynamic of the feed conversion coefficient
Summary
The aim of this study is to investigate some aspects of ontogenetic growth in pigs by analysing dynamic of growth from 30 kg live weight up to the maximum weight. The model concerns the nutritional aspects of growth. It was formulated by combining standard continuum methods, and discrete-time difference equations techniques. The following two focal variables are explicitly included in the formulation, an invariant of growth, and a feed conversion coefficient. Functional relations between relevant variables found in the experiments and field observations have been analysed. The novelty of the study is an innovative concept of the growth dynamic, and an approach to analysing bifurcation of the growth trajectory in pigs' ontogeny
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